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Multi-scale discrete approximation of Fourier integral operators

Andersson, Fredrik LU ; de Hoop, Maarten V and Wendt, Herwig (2012) In Multiscale Modeling & Simulation 10(1). p.111-135
Abstract (Swedish)
Abstract in Undetermined

We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost... (More)
Abstract in Undetermined

We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave packet transform. Numerical wave propagation and imaging examples illustrate our computational procedures. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
compression, reflection seismology, operator, separated representation, dyadic parabolic decomposition, wave packets, Fourier integral operators, multiscale computations
in
Multiscale Modeling & Simulation
volume
10
issue
1
pages
111 - 135
publisher
SIAM Publications
external identifiers
  • wos:000302183800006
  • scopus:84861516818
ISSN
1540-3459
DOI
10.1137/100808174
language
English
LU publication?
yes
id
93771e00-1307-4dca-bf7f-80031ed855e9 (old id 2224387)
date added to LUP
2011-12-16 21:49:19
date last changed
2017-01-22 03:13:45
@article{93771e00-1307-4dca-bf7f-80031ed855e9,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave packet transform. Numerical wave propagation and imaging examples illustrate our computational procedures.},
  author       = {Andersson, Fredrik and de Hoop, Maarten V and Wendt, Herwig},
  issn         = {1540-3459},
  keyword      = {compression,reflection seismology,operator,separated representation,dyadic parabolic decomposition,wave packets,Fourier integral operators,multiscale computations},
  language     = {eng},
  number       = {1},
  pages        = {111--135},
  publisher    = {SIAM Publications},
  series       = {Multiscale Modeling & Simulation},
  title        = {Multi-scale discrete approximation of Fourier integral operators},
  url          = {http://dx.doi.org/10.1137/100808174},
  volume       = {10},
  year         = {2012},
}